Below are listed rank-two temperaments supported by the29edo patent val, below the indicated cutoff in TE badness.

5-limit temperaments with badness below 0.1

Listed is the wedgie and the TE badness times 1000 for three temperaments with badness less than 0.1.

Rank	Wedgie	Name	Badness	Commas
1	<<1 -8 -15]]	Helmholtz	4.259	32805/32768
2	<<3 5 1]]	Porcupine	30.778	250/243
3	<<4 -3 -14]]	Negri	86.856	16875/16384

7-limit temperaments with badness below 0.06

Listed is the wedgie and the TE badness times 1000 for 17 temperaments with badness less than 0.06.

Rank	Wedgie	Name	Badness	Commas
1	<<1 -8 -14 -15 -25 -10]]	Garibaldi	21.644	225/224 3125/3087
2	<<4 -3 2 -14 -8 13]]	Negri	26.483	49/48 225/224
3	<<5 -11 -12 -29 -33 3]]	Tritonic	47.578	225/224 50421/50000
4	<<7 -56 -69 -105 -129 -3]]		48.081	32805/32768 52734375/52706752
5	<<3 5 16 1 17 23]]	Porky	54.389	225/224 250/243
6	<<6 10 3 2 -12 -21]]	Nautilus	57.420	49/48 250/243

11-limit temperaments with badness below 0.05

Listed is the wedgie and the TE badness times 1000 for 17 temperaments with badness less than 0.05.

Rank	Wedgie	Name	Badness	Commas
1	<<1 -8 -14 -18 -15 -25 -32 -10 -14 -2]]	Cassandra	23.556	100/99 225/224 245/242
2	<<5 -11 -12 -3 -29 -33 -22 3 31 33]]	Tritonic	23.659	121/120 225/224 441/440
3	<<6 10 3 8 2 -12 -8 -21 -16 12]]	Nautilus	26.023	49/48 55/54 100/99
4	<<3 5 16 4 1 17 -4 23 -8 -44]]	Porky	27.268	55/54 100/99 225/224
5	<<6 -19 -26 -21 -44 -58 -54 -7 17 31]]	Marvolo	28.965	225/224 441/440 4000/3993
6	<<0 29 29 29 46 46 46 -14 -33 -19]]	Mystery	34.291	441/440 896/891 3388/3375
7	<<4 -3 2 15 -14 -8 10 13 45 35]]	Negroni	35.296	49/48 55/54 225/224
8	<<14 -112 -138 -107 -210 -258 -218 -6 139 177]]		35.867	32805/32768 43923/43904 151263/151250
9	<<1 21 15 11 31 21 14 -24 -47 -21]]	Leapday	38.6240	121/120 441/440 686/675
10	<<4 -3 2 -14 -14 -8 -36 13 -22 -46]]	Negril	38.679	49/48 100/99 225/224
11	<<5 18 17 26 17 13 24 -11 -2 14]]		40.485	100/99 245/242 686/675
12	<<8 -6 4 1 -28 -16 -26 26 23 -11]]	Wilsec	41.886	49/48 121/120 225/224
13	<<6 -48 -55 -50 -90 -104 -100 7 50 50]]		45.457	441/440 4000/3993 235298/234375
14	<<9 15 19 12 3 5 -12 2 -24 -32]]	Ammonite	45.694	55/54 100/99 686/675
15	<<5 -40 -41 -32 -75 -79 -68 17 64 52]]		47.064	441/440 3388/3375 35937/35840
16	<<8 -93 -112 -86 -166 -200 -164 1 122 146]]		48.756	42592/42525 43923/43904 151263/151250
17	<<3 5 -13 4 1 -29 -4 -44 -8 56]]	Coendou	49.669	55/54 100/99 525/512

13-limit temperaments with badness below 0.04

Listed is the wedgie and the TE badness times 1000 for 43 temperaments with badness less than 0.04.

Rank	Wedgie	Name	Badness	Commas
1	<<0 29 29 29 29 46 46 46 46 -14 -33 -40 -19 -26 -7]]	Mystery	18.591	196/195 352/351 364/363 676/675
2	<<1 -8 -14 -18 -21 -15 -25 -32 -37 -10 -14 -19 -2 -7 -6]]	Cassandra	20.749	100/99 105/104 196/195 245/242
3	<<6 -19 -26 -21 -10 -44 -58 -54 -38 -7 17 47 31 68 43]]	Marvolo	21.470	169/168 225/224 364/363 441/440
4	<<4 -3 2 15 3 -14 -8 10 -10 13 45 18 35 1 -45]]		21.559	49/48 55/54 65/64 91/90
5	<<6 10 3 8 19 2 -12 -8 8 -21 -16 7 12 42 36]]	Nautilus	22.285	49/48 55/54 91/90 100/99
6	<<5 -11 -12 -3 -18 -29 -33 -22 -47 3 31 -1 33 -6 -51]]	Tritonic	22.993	105/104 121/120 196/195 275/273
7	<<4 -3 2 -14 3 -14 -8 -36 -10 13 -22 18 -46 1 62]]	Negril	24.383	49/48 65/64 91/90 875/858
8	<<1 21 15 11 8 31 21 14 9 -24 -47 -59 -21 -33 -13]]	Leapday	24.732	91/90 121/120 169/168 441/440
9	<<8 -6 4 1 6 -28 -16 -26 -20 26 23 36 -11 2 17]]	Wilsec	25.192	49/48 65/64 91/90 121/120
10	<<6 -48 -55 -50 -39 -90 -104 -100 -84 7 50 87 50 94 50]]	Sextilififths	25.276	364/363 441/440 676/675 10985/10976
11	<<3 5 16 4 -5 1 17 -4 -19 23 -8 -30 -44 -73 -32]]		26.543	55/54 65/64 91/90 100/99
12	<<5 18 17 26 11 17 13 24 -1 -11 -2 -41 14 -32 -58]]		26.929	91/90 100/99 169/168 245/242
13	<<9 15 19 12 14 3 5 -12 -11 2 -24 -23 -32 -31 4]]	Ammonite	27.168	55/54 91/90 100/99 169/168
14	<<8 -93 -112 -86 -81 -166 -200 -164 -158 1 122 156 146 187 38]]		27.440	676/675 1001/1000 10648/10647 10985/10976
15	<<2 -16 -28 -7 -13 -30 -50 -18 -28 -20 39 29 77 67 -19]]		27.464	121/120 169/168 225/224 275/273
16	<<2 13 30 22 16 16 42 28 18 33 6 -11 -42 -66 -26]]		28.521	100/99 169/168 225/224 275/273
17	<<2 -45 -57 -36 -42 -76 -96 -64 -74 -6 72 69 96 93 -12]]		28.632	352/351 676/675 1001/1000 1331/1323
18	<<3 5 16 4 24 1 17 -4 27 23 -8 37 -44 8 68]]		29.097	55/54 100/99 105/104 196/195
19	<<7 2 -11 -10 -2 -13 -37 -40 -29 -31 -30 -12 10 35 30]]		30.043	65/64 100/99 105/104 245/242
20	<<3 5 -13 4 -5 1 -29 -4 -19 -44 -8 -30 56 34 -32]]		30.233	55/54 65/64 100/99 105/104
21	<<5 -11 -12 -3 11 -29 -33 -22 -1 3 31 66 33 75 49]]		32.324	65/64 91/90 121/120 441/440
22	<<11 -1 -9 5 1 -27 -45 -30 -39 -18 15 6 45 36 -15]]		32.611	65/64 105/104 121/120 275/273
23	<<2 13 1 22 16 16 -4 28 18 -34 6 -11 58 41 -26]]		33.196	49/48 91/90 100/99 847/845
24	<<1 -8 -14 -18 8 -15 -25 -32 9 -10 -14 48 -2 74 94]]		33.610	65/64 91/90 100/99 245/242
25	<<6 10 3 8 -10 2 -12 -8 -38 -21 -16 -60 12 -39 -64]]		33.723	49/48 55/54 65/64 100/99
26	<<9 -72 -97 -75 -73 -135 -179 -150 -149 -23 75 97 125 154 25]]		33.754	1375/1372 1575/1573 2080/2079 2200/2197
27	<<3 -24 -42 -25 -34 -45 -75 -50 -65 -30 25 10 75 60 -25]]		33.849	225/224 275/273 847/845 1331/1323
28	<<2 -16 1 -7 -13 -30 -4 -18 -28 47 39 29 -23 -40 -19]]		34.066	49/48 91/90 121/120 352/351
29	<<11 -30 -38 -24 -28 -73 -91 -76 -85 -4 48 46 64 62 -8]]		34.213	225/224 441/440 847/845 1001/1000
30	<<9 -14 -10 -17 -15 -43 -41 -58 -57 16 9 17 -13 -5 11]]		34.616	105/104 196/195 245/242 1001/1000
31	<<9 -101 -126 -104 -102 -181 -225 -196 -195 -9 108 137 144 180 32]]		34.999	1575/1573 2080/2079 2200/2197 31250/31213
32	<<4 26 31 15 32 32 38 10 36 -1 -55 -22 -65 -25 55]]		35.601	121/120 196/195 275/273 572/567
33	<<8 -64 -83 -57 -52 -120 -154 -118 -112 -13 89 116 127 161 31]]		35.729	676/675 1001/1000 1375/1372 10648/10647
34	<<8 23 33 30 35 18 30 20 26 12 -10 -4 -30 -24 10]]		36.319	100/99 196/195 275/273 1331/1323
35	<<10 7 5 23 22 -12 -20 2 -2 -8 29 25 47 43 -9]]		36.654	49/48 55/54 91/90 847/845
36	<<2 13 1 -7 16 16 -4 -18 18 -34 -61 -11 -23 41 81]]		37.078	49/48 55/54 91/90 896/891
37	<<7 -27 -40 -39 -31 -59 -83 -86 -75 -17 3 28 29 61 37]]		37.123	225/224 364/363 441/440 1875/1859
38	<<3 34 45 33 24 47 63 42 27 9 -41 -70 -63 -99 -39]]		37.629	169/168 352/351 364/363 1001/1000
39	<<11 -59 -67 -53 -57 -119 -137 -122 -131 10 81 86 83 88 -1]]		37.907	441/440 847/845 1001/1000 13365/13312
40	<<3 -53 -71 -54 -63 -91 -121 -96 -111 -16 58 50 94 86 -18]]		38.480	352/351 847/845 1375/1372 1575/1573
41	<<2 42 59 51 45 62 88 74 64 19 -27 -51 -61 -92 -33]]		38.801	352/351 364/363 676/675 1375/1372
42	<<4 -32 -27 -14 -26 -60 -54 -36 -56 27 78 58 54 27 -38]]		39.125	121/120 196/195 352/351 676/675
43	<<1 -8 -14 11 8 -15 -25 14 9 -10 53 48 79 74 -13]]		39.411	55/54 65/64 91/90 847/832